Configurational Internal Energy Research Articles

Role of vacancies in structural thermalization of binary and high-entropy alloys

Vacancy assisted atomic self-diffusion is a major structural thermalization mechanism in bulk metal alloys. Depending on alloy composition, the local atomic environments might stabilize vacancies to such extent that the vacancies become trapped and the atomic self-diffusion part of the thermalization process stalls. The consequence is that such alloys get kinetically trapped in disordered structures. In this study, we investigate equimolar AgAu, CuPt, AgPdPtIr, and AgAuCuPdPt alloy thermalizing using Metropolis Monte Carlo simulations in two approaches, one where the alloy structure changes through vacancy migration and one where the structure changes by swapping atomic pairs. By comparing the two approaches, we find that the vacancy is less effective at thermalizing alloys with more elements (i.e. AgPdPtIr and AgAuCuPdPt), more heterogeneous configurational internal energy distributions (i.e. CuPt and AgPdPtIr), and strong interactions between certain elements, e.g. Ir-Ir interactions in AgPdPtIr. In the case of AgPdPtIr, the vacancy cannot thermalize Ir-Ir neighbors even when the vacancy is mobile, because the vacancy has difficulty breaking individual Ir-Ir pairs apart.

Thermodynamic–Dynamic Interrelations in Glass-Forming Polymer Fluids

We utilize the lattice cluster theory (LCT) of polymer fluids to show that the configurational entropy, enthalpy, and internal energy are all closely interrelated, as suggested by recent measurements by Caruthers and Medvedev, so that the generalized entropy theory (GET) of glass formation, a combination of the LCT and Adam-Gibbs model, can be recast in terms of any of these thermodynamic properties as a matter of convenience. Thermodynamic scaling, a form of density-temperature scaling exhibited by dynamic and some thermodynamic properties, is used to assess which thermodynamic properties are most naturally linked to dynamics, and we explore the origin of this scaling by both direct calculations based on the GET and molecular dynamics simulations of a coarse-grained polymer model. Through a combination of our comprehensive modeling of thermodynamic properties using the LCT and the highly predictive GET model for how the fluid thermodynamics relate to its dynamics, along with simulation results confirming these theoretical frameworks, we obtain insights into thermodynamic aspects of collective motion and the slow $\beta$-relaxation processes of glass-forming liquids.

Generating Excess Protons in Microsolvated Acid Clusters under Ambient Conditions: An Issue of Configurational Entropy versus Internal Energy.

Acid dissociation, and thus liberation of excess protons in small water droplets, impacts on diverse fields such as interstellar, atmospheric or environmental chemistry. At cryogenic temperatures below 1 K, it is now well established that as few as four water molecules suffice to dissociate the generic strong acid HCl, yet temperature‐driven recombination sets in simply upon heating that cluster. Here, the fundamental question is posed of how many more water molecules are required to stabilize a hydrated excess proton at room temperature. Ab initio path integral simulations disclose that not five, but six water molecules are needed at 300 K to allow for HCl dissociation independently from nuclear quantum effects. In order to provide the molecular underpinnings of these observations, the classical and quantum free energy profiles were decomposed along the dissociation coordinate in terms of the corresponding internal energy and entropy profiles. What decides in the end about acid dissociation, and thus ion pair formation, in a specific microsolvated water cluster at room temperature is found to be a fierce competition between classical configurational entropy and internal energy, where the former stabilizes the undissociated state whereas the latter favors dissociation. It is expected that these are generic findings with broad implications on acid–base chemistry depending on temperature in small water assemblies.

Experimental results and theoretical statistical modeling of malachite green adsorption onto MCM–41 silica/rice husk composite modified by beta radiation

The effect of beta particles (β−) on the structure and adsorption properties of the synthetic MCM–41 silica with rice husk MCM–41/RH composite was investigated for the first time. Based on XRD, SEM, and zeta potential results, the energy of β–radiation was sufficient to produce a morphs composite (β–MCM–41/RH) with negative surface charge and irregular internal porous structure. The adsorption of malachite green (MG) by the β–MCM–41/RH composite was performed under different conditions of solution pH, shaking time, initial MG concentration, adsorbent dose, and temperature. Modification of the MCM–41/RH composite by radiation process enhanced its maximum uptake efficiency for MG from 29.68 to 97.11%. The pseudo-second-order model with a correlation coefficient (R2 = 0.999) fitted well the MG adsorption kinetic. Linear and non-linear forms of the traditional isotherm models showed that Freundlich equation described well the MG adsorption data. Different statistical physics models on the basis of the grand canonical ensemble were also applied for a deeper interpretation of the MG adsorption mechanism. Based on the fitting experimental results, monolayer with two energy sites was found to be the best model in describing the MG adsorption phenomena. Through this model, the number of adsorbed MG molecules per site, the density of receptor sites, the removed amount of MG at saturation, the concentration at half saturation, and the adsorption energy were determined. The measured adsorption energies (E1 = −18.345 and E2 = −15.43 kJ/mol) suggested that electrostatic attraction and hydrogen bond interactions were involved in adsorption process. The parameters of thermodynamic functions including the configurational entropy, free enthalpy, and internal energy indicated that the MG adsorption onto the β–MCM–41/RH composite was exothermic and spontaneous in nature.

On the representability problem and the physical meaning of coarse-grained models.

In coarse-grained (CG) models where certain fine-grained (FG, i.e., atomistic resolution) observables are not directly represented, one can nonetheless identify indirect the CG observables that capture the FG observable's dependence on CG coordinates. Often, in these cases it appears that a CG observable can be defined by analogy to an all-atom or FG observable, but the similarity is misleading and significantly undermines the interpretation of both bottom-up and top-down CG models. Such problems emerge especially clearly in the framework of the systematic bottom-up CG modeling, where a direct and transparent correspondence between FG and CG variables establishes precise conditions for consistency between CG observables and underlying FG models. Here we present and investigate these representability challenges and illustrate them via the bottom-up conceptual framework for several simple analytically tractable polymer models. The examples provide special focus on the observables of configurational internal energy, entropy, and pressure, which have been at the root of controversy in the CG literature, as well as discuss observables that would seem to be entirely missing in the CG representation but can nonetheless be correlated with CG behavior. Though we investigate these problems in the framework of systematic coarse-graining, the lessons apply to top-down CG modeling also, with crucial implications for simulation at constant pressure and surface tension and for the interpretations of structural and thermodynamic correlations for comparison to experiment.

The entropy of the rotational conformations of (poly)isoprene molecules and its relationship to rubber elasticity and temperature increase for moderate tensile or compressive strains

Molecular networks comprised of crosslinked cis-1,4 polyisoprene, often referred to as "natural rubber," are one of the most common systems for the study of rubber elasticity. Under moderate tensile or compressive strain, network chains begin to assume straighter paths, as local molecular kinks are removed. Isoprene units along the chain backbone are mechanically forced from their equilibrium distributions of 18 possible rotational states into a smaller subset of states, restricted to more linear conformations with the greatest end-to-end distances. There are two consequences to this change: both the configurational entropy and average internal energy decrease. We find that the change in entropy, and resulting change in free energy, gives rise to an elastic force. We derive an expression for a chain extension force constant that we have incorporated in an explicit, three-dimensional meso-scale network simulation code. Using this force model, our simulations predict a macroscopic stress-strain relationship that closely matches published experimental values. We also predict a slight increase in temperature resulting from the change in average internal energy in the affected isoprene units that is consistent with experiments.

Elucidation of conformational characteristics and configurational properties of poly((R)-3-hydroxybutyrate) by ab initio statistical mechanics

Conformational free energies and geometrical parameters derived from ab initio molecular orbital (MO) calculations for monomeric and dimeric model compounds of poly((R)-3-hydroxybutyrate) (PHB) were introduced into the refined rotational isomeric state (RIS) scheme to yield the characteristic ratio, configurational entropy, configurational internal energy, bond conformations and averaged geometrical parameters of PHB. The reliability of the MO calculations was confirmed through comparison with 1H and 13C nuclear magnetic resonance experiments for the monomeric model compound. The characteristic ratio (5.60) derived from the refined RIS calculations for the unperturbed PHB chain at 25 °C is in satisfactory agreement with the experimental values (6.1–6.3). The crystalline PHB chain is known to adopt the ttg+g+ conformation in the repeating unit. A previous study revealed that a trimeric (R)-3-hydroxybutyrate substrate bound on a PHB depolymerase lies in the ttg+g+ and tg−tt conformations. In our MO calculations, the former conformation is the most stable, and the latter is metastable but further stabilized by intermolecular C=O⋯H−N and C=O⋯H−O hydrogen bonds on the enzyme.

Theory and simulation for associating cyclic molecules

A successful equation of state for ring molecules [J. Chem. Phys. 101, 6880 (1994); Phys. Rev. E 50, 386 (1994)] is extended using Wertheim's first-order thermodynamic perturbation theory to predict the degree of bonding and thermodynamic properties of associating cyclic molecules. This new theory is tested against molecular simulation results for pure fluids of cyclic trimers with either one or three association sites. The trimers’ association potential of interaction is modeled by an orientation-dependent square-well, and the segment–segment interactions are of the hard-sphere type. A wide range of densities and temperatures is studied. Values for fraction of molecules not bonded, configurational internal energy and compressibility factor were obtained using Metropolis Monte Carlo simulations in the canonical and isothermal–isobaric ensembles. The theory predictions are in excellent agreement with these simulation results.

Self-consistent Ornstein-Zernike approximation for molecules with soft cores

The self-consistent Ornstein-Zernike approximation (SCOZA) is an accurate liquid state theory. So far it has been tied to interactions composed of hard core repulsion and long-range attraction, whereas real molecules have soft core repulsion at short distances. In the present work, this is taken into account through the introduction of an effective hard core with a diameter that depends upon temperature only. It is found that the contribution to the configurational internal energy due to the repulsive reference fluid is of prime importance and must be included in the thermodynamic self-consistency requirement on which SCOZA is based. An approximate but accurate evaluation of this contribution relies on the virial theorem to gauge the amplitude of the pair distribution function close to the molecular surface. Finally, the SCOZA equation is transformed by which the problem is reformulated in terms of the usual SCOZA with fixed hard core reference system and temperature-dependent interaction.

Statistical thermodynamics predictions of the solubility parameter

AbstractThe Simha and Somcynsky (S‐S) lattice‐hole theory has been shown to represent accurately the pressure–volume–temperature (PVT) surface of chain molecular melts and their mixtures. The characteristic scaling parameters, P*, T* and V*, extracted from equation of state (eos) measurements, are known for a large number of polymers. On this basis it is possible to compute the configurational internal energy density and thus the solubility parameter δ as a function of temperature and pressure, δ = δ(T, P). In the first part of this paper it is shown that the theory leads to an energy approximately proportional to the first power of density, that is of the van der Waals type, as found for low molar mass fluids by Hildebrand. We continue with a computation of δ for a series of polymer melts at two levels of temperature, namely T = 25 °C and T = Tg + 300 K. Next, the results are compared with those listed in reference publications, all at ambient pressure. The theoretical values extrapolated from the melt to 25 °C were systematically higher than those listed. However, good correlation is obtained with the high‐temperature calculations for a large variety of polymers. Arguments for this low–high temperature correlation are presented in terms of corresponding levels of molecular mobility and packing in solution and in bulk. Copyright © 2004 Society of Chemical Industry

Square-well chain mixture: analytic equation of state and Monte Carlo simulation data

An analytic perturbation theory equation of state developed for mixtures of freely-jointed square-well chain fluids of variable well width is tested against Monte Carlo simulation data. The equation of state is based on second-order Barker and Henderson perturbation theory to calculate the thermodynamic properties of the reference sphere fluid, and on first-order Wertheim thermodynamic perturbation theory to account for the connectivity of spheres to form chains. A real function expression for the radial distribution function of hard spheres and one-fluid type mixing rule are used to obtain an analytic, closed form expression, for the Helmholtz free energy of mixtures of square-well spheres. In order to test the theories, Monte Carlo simulations for binary mixtures of square-well chains were performed to obtain the radial distribution function at the contact point, the compressibility factor, and the configurational internal energy of these mixtures. The proposed equation of state leads to good predictions of compressibility factor of square-well chains and their mixtures when compared with the simulation data.

Diffusion reordering kinetics in lattice-gas systems: Time evolution of configurational entropy and internal energy

The reordering kinetics of a diffusion lattice-gas system of adsorbates with nearest- and next-nearest-neighbor interactions on a square lattice is studied within a dynamic Monte Carlo simulation, as it evolves towards the equilibrium from a given initial configuration, at a constant temperature. The diffusion kinetics proceeds through adsorbate hoppings to empty nearest-neighboring sites (Kawasaki dynamics). The Monte Carlo procedure allows a ``real'' time definition from the local transition rates, and the configurational entropy and internal energy can be obtained from the lattice configuration at any instant $t$ by counting the local clusters and using the ${C}_{2}$ approximation of the cluster variation method. These state functions are then used in their nonequilibrium form as a direct measure of reordering along the time. Different reordering processes are analyzed within this approach, presenting a rich variety of behaviors. It can also be shown that the time derivative of entropy (times temperature) is always equal to or lower than the time derivative of energy, and that the reordering path is always strongly dependent on the initial order, presenting in some cases an ``invariance'' of the entropy function to the magnitude of the interactions as far as the final order is unaltered.

Engineering a simple polarizable model for the molecular simulation of water applicable over wide ranges of state conditions

We perform a systematic analysis of the relationship between the molecular geometry, the force-field parameters, the magnitude of the induced dipoles, and the resulting site–site microstructure of a model for water consisting of simple point charges plus a self-consistent point dipole polarizability. We constrain the model to represent the experimental values of the pressure and the configurational internal energy of water at ambient conditions, while keeping a permanent dipole moment of 1.85 D. The resulting force fields are then used to perform additional simulations at high temperature to determine the effect of polarizabilities on the site–site structure, and to make contact with neutron scattering experiments as well as ab initio simulation results. We show that the parameterization of the model is possible for 0≤ROM≤0.25 Å, where ROM is the oxygen-to-negative charge distance along the bisectrix of the H–O–H angle, resulting in total dipole moments from 2.88 to 3.03 D, with polarization energies accounting for 40%–57% of the total configuration internal energy of water. These results, in conjunction with the behavior of the short range site–site correlation functions, highlight the shortcomings of the simple point charge approximation for the polarization behavior at short intermolecular distances, and give a meaningful reference from which we can attempt to overcome these defects.

First-principles calculation of the pressure dependence of phase equilibria in the Al-Li system.

The solid-phase portion of the Al-Li phase diagram has been computed from first principles both at zero pressure and at a hydrostatic compression of 5.4 GPa. Computation of the pressure dependence of the Al-Li phase equilibria answers two questions: (1) how important is the effect of the atomic size difference, and (2) is the stability of the ${\mathrm{Al}}_{3}$Li precipitates influenced by high hydrostatic stress. The zero-pressure first-principles phase diagram exhibits excellent qualitative agreement with experimental data. The presence or absence of solid solutions (SS), of stable and metastable intermetallic phases, and their degree of order are computed correctly. Compression is predicted to affect the phase equilibria in Al-Li as follows: (1) the solubility of Li in fcc Al-rich SS is decreased, (2) the solubility of Al in Li is increased. However, the low melting point of Li limits the range of SS, and (3) the metastable ${\mathrm{Al}}_{3}$Li Al-rich fcc SS phase equilibrium is unaffected and the stability of the precipitates is unchanged, (4) the ordering tendencies at Li-rich compositions are slightly enhanced. Although high pressure eliminates the difference in atomic volume of the pure constituents, it has almost no effect on the solid-solid phase equilibria in this alloy system. A simple method for verifying the accuracy of the cluster expansion for the configurational internal energy is presented and applied. Moreover, it has been shown that with a convenient choice of the occupation numbers, one can define correlation functions which greatly facilitate the determination of new ground state structures. \textcopyright{} 1996 The American Physical Society.

Extension of the SWLE equation of state to property calculations for soft-core fluids

Abstract Shen, S. and Lu, B.C.-Y., 1993. Extension of the SWLE equation of state to property calculations for soft-core fluids. Fluid Phase Equilibria 86: 27-46 The previously developed four-parameter perturbed hard-sphere equation of state based on the square-well-linear-extension (SWLE) potential is extended to the property calculations for soft-core fluids. The predicted values of configurational Helmholtz free energy, configurational internal energy, compressibility factor and second virial coefficient for the Lennard-Jones fluid over a wide range of reduced density (ϱ ★ = 0.02–2.50) and reduced temperature ( T ★ = 0.591–100) are in good agreement with the computer simulation data. The predicted values of configurational internal energy (ϱ ★ =0.1–1.25, T ★ = 0.81169–811.69) and compressibility factor (ϱ ★ = 0.6–0.7, T ★ = 0.81169–811.69) for the modified Buckingham (6-exp) fluid are also satisfactory. For data correlation, the SWLE equation yields comparable accuracy with the 33-parameter equation of Adachi et al. (1988), [Adachi Y., Fijhara, T., Takamiya, M. and Nakanishi, K., 1988. Generalized equations of state for Lennard-Jones Fluids. I. Pure fluids and simple mixture. Fluid Phase Equilibria, 39: 1-38], based on the investigated thermodynamic properties of the Lennard-Jones fluid.

Computer simulation of molecular fluid mixtures: Results and two new one‐fluid models

AbstractMonte Carlo simulation results for binary mixtures of diatomic molecules with spheres, diatomic molecules of different bond lengths, and triatomic molecules with spheres, all interacting with the site‐site Lennard‐Jones potential, were obtained at three different volume ratios and a range of densities and compositions. We report the configurational internal energy of the mixture and of the 1‐1, 1‐2 and 2‐2 pairs, and the compressibility factors at 195 state points. The site‐site correlation functions also computed are available from the authors. Equations of state derived previously (Sowers and Sandler, 1991, 1992) for pure site‐site Lennard‐Jones fluids from a combination of perturbation theory and a three‐parameter corresponding states principle are extended to mixtures using simple one‐fluid mixing rules. These simple mixing rules allow us to make satisfactory predictions of the compressibilities computed from simulation without the use of binary interaction parameters. We also show that the effect of composition on the perturbation free energy βAp/N not accounted for by one‐fluid mixing rules is quite small, and therefore a more complicated mixing rule is not necessary in our equations of state for the mixtures studied.

Phase stability of dense multicomponent charged and uncharged hard-sphere fluid mixtures

We report calculations of the phase diagram and spinodal decomposition line of a charged hard-sphere fluid mixture constituted of two different cations, one anion and one neutral particle species. In the high-density regime the model is suitable to mimic molten silicate and metal halides mixtures, as those forming a magmatic fluid; in the low-density regime it can conveniently describe the properties of charged colloidal suspensions or micellar solutions. In this work the attention is focused mainly on the high-density regime of the mixture, and phase stability conditions are determined through the knowledge of the Gibbs free energy of mixing, Gmix at constant pressure, as calculated in the mean spherical approximation. It turns out that the solubility of the neutral component in the ionic mixture depends substantially on the potential-to-kinetic-energy ratio, that is, on the so-called coupling strength or plasma parameter, and increases when this decreases. This result is rationalized by considering the different terms contributing to Gmix and, specifically, the confi-gurational Coulombic internal energy term and entropic term. The fine balance between these two quantities is detailed and the onset of phase segregation discussed on these same bases. Such a representation also allows us to interpret why mixtures like those envisaged here are characterized by a phase diagram with an upper consolution point and why the critical temperature turns out to be an increasing function of the pressure. The implications of this last result seem interesting since, e.g., molten salt-silicate mixtures and, therefore, presumably fused rocks or magmas, could segregate not only under cooling, but also at constant temperature as the result of pressure variations.

On the thermodynamic properties of several two-dimensional Ising lattices

The thermodynamic properties of the triangular, square and honeycomb lattices have been investigated. Numerical results involving the temperature dependence of the equilibrium surface pressure, the configurational free energy, entropy, internal energy and specific heat are presented and discussed.

Atomic ordering in non-stoichiometric solid solutions in the low-temperature range

An expansion is found of the configurational internal energy of a system. The expansion is carried out within long-range ordering parameters and static correlation functions. The results obtained are demonstrated by a specific example — an analysis of the carbon martensite. A number of peculiarities are shown numerically for the low-temperature range related to the behaviour of short- and long-range ordering parameters and, in particular, the major role played by short-range ordering.

Perturbation calculation of thermodynamic properties of liquid benzene using the six centre Lennard-Jones potential

The thermodynamic properties and structure of liquid benzene have been studied by means of the nonspherical perturbation theory due to Fischer after modelling it as a fused sphere body with the six centre Lennard-Jones potential. It is shown that the perturbation theory is capable of predicting the liquid density within a few per cent of that obtained from molecular dynamics simulation. Also, the calculated sound velocity as a function of pressure and temperature is in good agreement with the experimental data. However, the theory is found to be less satisfactory for structure prediction which leads to large errors in the predicted configurational internal energy.